Homogenization Transport by Random Flows
Abstract. We shall discuss several asymptotic problems for transport by stochastic flows. We prove the long time diffusive behavior for flows, which are Markovian in time. Next, for periodic stochastic flows we prove the Central Limit Theorem which holds with respect to the randomness in the initial conditions, for almost every realization of the flow. Finally we describe the limiting shape of a set carried by the flow. The latter results are joint with D. Dolgopyat and V. Kaloshin.